Noticing Patterns
Summing Consecutive Numbers
Age 11 to 14
Challenge Level 
This problem offers a simple context for students to explore, make generalisations and prove conjectures, working numerically and algebraically.
1 Step 2 Step
Age 11 to 14
Challenge Level
This problem is inaccessible without looking at simpler cases, and thus helps students to see the value of specialising in order to generalise.
Pick's Theorem
Age 14 to 16
Challenge Level
This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.
What's Possible?
Age 14 to 16
Challenge Level
As well as introducing the difference of two squares, this problem allows students to explore, conjecture and use algebra to justify their results.